Influence of attenuation on the generation of optical vortices in multihelicoidal optical fibers

In this paper we have studied influence of attenuation on conversion processes of the fundamental mode (FM) in multihelicoidal optical fibers (MHF) in the vicinity of the point of accidental spectrum degeneracy within the framework of the scalar approximation. To this end, we have obtained expressions for modes of the MHF, which consist of the FM and an optical vortex (OV), and shown that conversion of the FM into the OV takes place. The difference in the attenuation coefficients for the partial fields of MHF’s modes leads to deterioration in the conversion process even with an ideal system’s tuning. At sufficiently large values of attenuation coefficients the conversion of the incoming FM into the vortex vanishes. Also we have shown the presence of exceptional point (EP) in the spectra of modes of the MHF and demonstrated enhanced sensitivity of the fiber in the vicinity of the EP to perturbations.

Imperfections of Scalar Approximation in Calibration of Computer-Generated Holograms for Optical Surface Measurements

Computer-generated hologram (CGH) null correctors are used as accuracy standards for interferometric measurements of optical surfaces and optical systems. Diffractive optics calibrators (DOCs) have been developed to evaluate the phase tolerance of CGHs based on scalar approximation by measuring variations in duty cycle and etching depth. However, if the grating period of a CGH < 5 λ, the scalar approximation is not accurate for phase analysis and reconstruction. In this study, the measurement errors of DOCs with small-period CGHs were investigated and experimentally verified. Results show that the imperfections of scalar approximation in CGHs cannot be ignored and the development of rigorous evaluation methods to improve the measurement accuracy of CGHs is of great practical significance.

An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems

Based on a modified secant equation, we propose a scalar approximation of the Hessian to be used in the trust region subproblem. Then, we suggest an adaptive nonmonotone trust region algorithm with a simple quadratic model. Under proper conditions, it is briefly shown that the proposed algorithm is globally and locally superlinearly convergent. Numerical experiments are done on a set of unconstrained optimization test problems of the CUTEr collection, using the Dolan-Moré performance profile. They demonstrate efficiency of the proposed algorithm.

A Neural Network Correction to the Scalar Approximation in Radiative Transfer

The next generation of advanced high-resolution sensors in geostationary orbit will gather detailed information for studying the Earth system. There is an increasing desire to perform observing system simulation experiments (OSSEs) for new sensors during the development phase of the mission in order to better leverage information content from the new and existing sensors. Forward radiative transfer calculations that simulate the observing characteristics of a new instrument are the first step to an OSSE, and they are computationally intensive. The scalar approximation to the radiative transfer equation, a simplification of the vector representation, can save considerable computational cost, but produces errors in top of the atmosphere (TOA) radiance as large as 10% due to neglecting polarization effects. This article presents an artificial neural network technique to correct scalar TOA radiance over both land and ocean surfaces to within 1% of vector-calculated radiance. A neural network was trained on a database of scalar–vector TOA radiance differences at a large range of solar and viewing angles for several thousand realistic atmospheric vertical profiles that were sampled from a high-resolution (7 km) global atmospheric transport model. The profiles include Rayleigh scattering and aerosol scattering and absorption. Training and validation of the neural network was demonstrated for two wavelengths in the ultraviolet–visible (UV-Vis) spectral range (354 and 670 nm). The significant computational savings accrued from using a scalar approximation plus neural network correction approach to simulating TOA radiance will make feasible hyperspectral forward simulations of high-resolution sensors on geostationary satellites, such as Tropospheric Emissions: Monitoring of Pollution (TEMPO), GOES-R, Geostationary Environmental Monitoring Spectrometer (GEMS), and Sentinel-4.

Light as a wave

This chapter introduces the basic concepts, such as light as a wave, a brief overview of Maxwell’s equations, the harmonic wave solution, spatial frequency, phasors, intensity, complex representation, the scalar approximation, and light quanta.